Doesn’t he look like a puppet? In fact the correct term is ‘marionette’ – for a puppet on strings, worked from above. But who’s pulling Nick Clegg’s strings this time?

The Government is running an independent study into the impact of the Bedroom Tax, in order to find out if it is really possible for social housing tenants to move into smaller accommodation to escape its effects. The result should more likely be feared than welcomed.

Nick Clegg announced that the study was taking place in response to a Parliamentary question from Harriet Harman – but was immediately undermined by the Department for Work and Pensions. A government spokesman said the DWP routinely commissions research on new policies and an independent consortium was already carrying out evaluation work.

Clegg had to say he was taking action after his own party voted to change its policy on the Tax – the Liberal Democrats now oppose it – but this is not cause for celebration.

Who will carry out this independent study? We are told it is an “independent consortium” but what does that mean? What will be their terms of reference? What questions will they be asking and will they be the questions that need to be asked?

Observers should be raising serious doubts about all of these because this is not a government with a good track record on evidence-led policy.

We all know what this is about – the government’s hugely flawed scheme to claw back Housing Benefit cash from social housing tenants, taking 14 per cent of payments from those with one spare bedroom, and a quarter of the benefit from anyone with two. The Discretionary Housing Payment scheme for local councils was boosted to £60 million in anticipation of extra demand from struggling tenants.

It is true that evidence about the policy is conflicting. Lord Freud, introducing it in the House of Lords, apparently refused to listen to arguments that there were too few single-bedroom properties into which under-occupiers could downsize. Now he is blaming local authorities for the shortage.

The government said the policy would save £480 million, but the increased cost of DHPs must be subtracted from that, and also the costs of people who do manage to downsize. This could range from just four per cent of the 660,000 affected households to 20 per cent, depending on who you believe – a recent study by the University of York suggested that 20 per cent of households intended to move (which isn’t quite the same as actually doing it), but this was based on evidence from just four housing associations.

It seems unlikely that one-fifth of everyone affected nationally is moving to a different property – but even if they were, this would not create a saving for the government because it would have to pay out, not only increased Housing Benefit for those who have moved into smaller but more expensive private rented housing, but also Housing Benefit for people moving into the now-vacant larger social housing.

And then there are the people who cannot downsize but cannot afford the rent if their Housing Benefit is reduced. Recent reports had 50,000 households facing eviction – around one-thirteenth of the total number affected.

If they become homeless, local councils will have to find temporary accommodation for them – and this is paradoxically much more expensive than putting them in social housing, because they have to go into bed-and-breakfast rooms. Homelessness was already on the increase before the Bedroom Tax was introduced, rising from 44,160 households in 2011-12 to 53,540 in 2012-13.